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Introduction
Predictive Margins and Their Pictures
Conclusion
How to get an edge with margins and marginsplot
Bill Rising
StataCorp LP
2012 UK Stata Users Group Meeting
London
13 September 2012
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Goals
Getting Started
This will be an interactive demonstration
We want to explore the margins command
On the way we will learn about making nice graphs to help with
explanations
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Goals
Getting Ready
We’ll be doing a lot of work with categorical variables
By default, Stata does not show the base reference class when
using factor variables
Let’s fix this
. set showbaselevels on, permanently
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Starting Simple
We will start with the low birthweight dataset from Hosmer and
Lemeshow’s book on logistic regression
. webuse lbw
We can take a peek at the dataset
. codebook, compact
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Linear Regression Coefficients
Let’s start simple with an easy linear regression for birthweights
. regress bwt c.age##c.age lwt i.smoke i.race
We know what the coefficients mean
The coefficient for 1.smoke says: all other things being equal (i.e.
weight and race), we think smokers’ babies are about 400 lighter
than non-smokers’ babies
We can see that age looks to have a quadratic effect
It would be nice to see this more clearly
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Asking a Different Question
Now suppose instead of being asked about the effect of age, we
are asked
“What would the model take for the average weight of a baby for
a mother aged 30?”
There are two paths we can take here:
We could plug in 30 for the age for all the women in our sample,
leave all other covariates the same, predict the birthweights, and
average the results
Order: predict with partial info, then average
We could average all the other covariates, set age to 30, and
predict
Order: average, then predict with partial info
The first path is called ‘predictive margins’ or ‘average predictive
margins’—it is the one we will take
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
A Predictive Margin
Stata implements predictive margins using the margins
command
Here is what we could use as our best guess of the mean weight
of babies of women aged 30:
. margins, at(age==30)
Computationally, the point estimate could be computed by
Changing age to 30 everywhere
Using predict to get predicted values
Finding the mean of those values
margins does more—it computes standard errors
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Margins Across Multiple Values
One of the nice things about margins is that it can be used get
average predicted values over a range
This, in some way, is a way to see a variable’s effect over a range
of values
So, for example, if we wanted to show someone how birthweights
change by mother’s age, we could make the following table
. margins, at(age==(15(5)45))
This lets us see the weights drop and then rise
But it forces us to use factor variable-like notation for the ages
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Picturing Predictive Margins
Stata has a command which can draw graphs arising from the
margins command: marginsplot
Here is a very simple example
. marginsplot
This gives a good view of the parabolic shape
We will now investigate margins
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
What About Comparing Groups?
Suppose we would like to compare weights across the three race
categories
This is done by including race in the varlist for the margins
command:
. margins race
We can do this because we specified i.race in the model
Aside: this is equivalent to the following
. margins, at(race==1) at(race==2) at(race==3)
These values can be interpreted as best-guesses for partial
information for your sample
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Graphing the Group Means
We can graph these using marginsplot
. marginsplot
2400
2600
Linear Prediction
2800
3000
3200
3400
Predictive Margins of race with 95% CIs
white
black
race
other
The graph is a little odd to see
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Making a Nicer Graph
We can get this graph to look nicer by
Squelching the connecting lines with recast(scatter)
Expanding the horizontal axis with the xscale option
Here is a prettier graph
Predictive Margins of race with 95% CIs
2400
2600
Linear Prediction
2800
3000
3200
3400
. marginsplot, recast(scatter) xscale(range(0.5 3.5))
white
Bill Rising
black
race
other
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
More Complex Margins
There is no reason for us to limit our predictive margins to be
computed over just one variable
We could just as well look to see how age and smoking status
work together
Here is the the margins command
. margins smoke, at(age==(15(5)45))
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Still a Simple Graph
The marginsplot still makes a simple graph
. marginsplot
2500
3000
Linear Prediction
3500 4000 4500
5000
Predictive Margins of smoke with 95% CIs
15
20
25
30
age of mother
smoke=0
35
40
45
smoke=1
The confidence intervals overlap a bit
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Driving the Point Home
If we wanted to specify smoking and age, we could use the
interaction notation in the margins command
This is true even though there were no interactions—all that is
done is that all possible combinations of smoking status and race
are included
The command is not bad. . .
. margins race#smoke, at(age==(15(5)45))
. . . but the output is
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
We Can Still Visualize This
We can still make a picture
. marginsplot, noci
2500
Linear Prediction
3000 3500 4000
4500
Predictive Margins of race#smoke
15
20
25
30
age of mother
white, smoke=0
black, smoke=0
other, smoke=0
35
40
45
white, smoke=1
black, smoke=1
other, smoke=1
The noci option squelches the confidence intervals to make a
better graph
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
A Fancy Overlay
In this particular dataset, there is an outlier: a combination of a
woman who is much older with a baby whichi is much heavier
We can make a graph which shows the effect of age together
with a scatterplot
. quietly margins, at(age==(15(1)45))
. marginsplot, legend(off) ///
addplot(scatter bwt age, mcolor(gs12) below)
1000
Linear Prediction
2000
3000
4000
5000
Predictive Margins with 95% CIs
10
20
Bill Rising
30
age of mother
40
50
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
A Richer Dataset
Now will switch over to the nhanes2 dataset
. webuse nhanes2
This is a nice dataset, because it has good things for both linear
and logistic regression
These are survey data
. svyset
We will need to use the svy: prefix for estimation
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Looking at Diabetes
Now we would like to look at the chances of having diabetes
Here is a simple model
. svy: logistic diabetes age i.sex i.race bmi
We can see that age and bmi both increase the odds of diabetes
by about 6% for each unit increase
How does this play out for race and age?
. margins race, at(age==(20(5)75)) vce(uncond)
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Here Is the Picture
We can get a nice picture
. marginsplot, legend(rows(1))
0
.05
Pr(Diabetes)
.1
.15
.2
.25
Predictive Margins of race with 95% CIs
20
25
30
35
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White
Bill Rising
45
50
age in years
Black
55
60
65
Other
Margins and marginsplot
70
75
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
This is Better than Odds Ratios
This type of graph is something that makes explaining a logistic
model much easier than via odds ratios
It is as applicable to the general population as much as your
belief that your sample is representative of the general population
Which is important for the odds ratios also
Here, a picture is worth a thousand hard words
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
For Probit Fans
If you prefer probit models, we can use the same type of logic
. svy: probit diabetes age i.sex i.race bmi
Now the coefficients are not very interpretable
We can still get margins
. margins race, at(age==(20(5)75)) vce(uncond)
Creating the predictive margins still works the same
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Picturing a Probit
We can still get a very similar nice picture
. marginsplot, legend(rows(1))
0
.05
Pr(Diabetes)
.1
.15
.2
.25
Predictive Margins of race with 95% CIs
20
25
30
35
40
White
Bill Rising
45
50
age in years
Black
55
60
65
Other
Margins and marginsplot
70
75
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Interactions
Here is a model with interactions
. svy: logit diabetes c.age##c.age##race bmi i.sex
If we look at the output, the higher-level interactions are needed
in the model
They are nearly impossible to picture or to talk about, however
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Visualizing Interactions with marginsplot
Here are the margins for this complex model
. margins race, at(age==(20(5)75)) vce(uncond)
And a nice, informative picture
. marginsplot, legend(rows(1))
0
Pr(Diabetes)
.1
.2
.3
Predictive Margins of race with 95% CIs
20
25
30
35
40
White
Bill Rising
45
50
age in years
Black
55
60
65
Other
Margins and marginsplot
70
75
Introduction
Predictive Margins and Their Pictures
Conclusion
Introducing Predictive Margins
Non-Linear Models
Bothered by Counterfactuals
You might have been bothered by the idea in the preceding
examples that we used
. margins race, ...
This sets every observtion to each race category while computing
the predictive margins
If you would rather compute the predictive margins within each
race, use the over option
. margins, at(age==(20(5)75)) vce(uncond) over(race)
The differences from before are small, and the picture is similar
(not shown in handouts)
. marginsplot, legend(rows(1))
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Conclusion
Conclusion
marginsplot is very good for showing how models work
This can be used to good effect when explaining even simple
non-linear models
This can be used to good effect when explaining any type of
interactions
Bill Rising
Margins and marginsplot
Introduction
Predictive Margins and Their Pictures
Conclusion
Conclusion
A Fun Plot
Just For Fun
Believe it or not, it is possible to make a contour plot of predictive
margins
. do margcon
80
Here is the picture
.5
60
.4
age in years
40
.35
.3
.25
.2
.15
.1
20
.05
0
10
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Body Mass Index (BMI)
Bill Rising
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Margins and marginsplot
Pr(diabetes), predict()
.45